N8
MATHEMATICS
SUPPORT CENTRE
Title: Ratio
Target: On completion of this worksheet you should be able to simplify ratios and
divide a quantity in a given ratio.
If one student has £15 and his friend has £5
then he has 3 times as much as his friend. We
can say that the amounts they have are in the
ratio of 3 to 1. This is written as 3:1.
Note that the original amounts are cancelled to
their lowest terms.
Examples
Write the following ratios in their lowest terms:
1. 4:8
Divide both parts by 4 to give 1:2
You can use the fraction button on your
calculator:
4 ab/c 8 =
This gives the answer 1:2 but note that the
symbol between the numbers will be the
symbol your calculator uses for fractions.
2. 20:25
20:25 = 4:5
( dividing by 5 )
3. 36:27
36:27 = 4:3 ( dividing by 9 )
If you use your calculator the answer will
appear as a mixed number ( 1 13 but in
calculator notation) so use the d/c button to
change to an improper fraction (usually this is
above the fraction button in which case you
will need to use shift, 2nd function or inv ).
4. 15m:50cm
The units must be the same so convert 15m to
centimetres ie 15m = 1500cm
1500:50 = 30:1
J.Reed,Coventry University,October2000
Exercise
Write the following ratios in their lowest terms:
1. 3:18
2. 35:15
3. 14:49
4. 10:1000
5. 12:15
6. 60:36
7. 50p:£1
8. 250m:1·5km
( Answers: 1:6, 7:3, 2:7, 1:100, 4:5, 5:3, 1:2,
1:6 )
Examples
1. Divide £120 in the ratio 1:3
We need to divide £120 into equal parts so that
A has 1 part and B has 3 parts.
We need 1 + 3 = 4 parts altogether.
1 part = £120 ÷ 4
= £30
A has £30 and B has £30 × 3 = £90
To divide a given amount in a given ratio
•
•
•
Add the parts of the ratio
Divide the amount by this total
Multiply this by each part of the ratio
2. Alan, Ali and Arthur are going to divide
£450 in the ratio 5:2:3. How much do they
each receive?
5 + 2 + 3 = 10 (add the parts of the ratio)
450 ÷ 10 = 45 (divide to find one part)
Alan receives £45 × 5 = £225
Ali receives £45 × 2 = £90
Arthur receives £45 × 3 = £ 135
( Check: 225 + 90 + 135 = 450 )
Exercise
1.
2.
3.
4.
Divide 24 in the ratio 1:5
Divide 72 in the ratio 5:3
Divide £540 in the ratio 1:8
Tom and Jasmine are going to divide
their earnings in the ratio of the time
each spent working. Tom spent 6 hours
and Jasmine spent 8 hours. Their total
earnings are £105. How much does
each receive?
5. Ninety tulip bulbs are to be planted in a
garden. There are three colours: red,
yellow and pink and these are to be
planted in the ratio of 2:4:3. How many
yellow tulips are there?
( Answers: 4 & 20, 45 & 27, £60 & £480, Tom
gets £45 & Jasmine gets £60, 40 )
Examples
1. Two students A and B divide a sum of
money in the ratio 2:5. B receives £20. What
is the total sum of money?
B receives 5 parts which is £20 so
1 part = £20 ÷ 5
= £4
Exercise
1. A sum of money is divided between
two students A and B in the ratio 2:3. If
A receives £48 how much does B
receive?
2. A box of chocolates contains soft
centres and hard centres in the ratio 4:5.
If there are 20 chocolates with hard
centres how many chocolates are there
altogether?
3. A student is writing an essay and
divides her time between planning and
writing in the ratio 1:2. If she spends
50 minutes planning the essay how long
does she spend writing it?
4. A small company divides its profits
between the three directors in the ratio
3:2:6. The director with the smallest
amount receives £24300. How much
do the other two directors receive?
5. Red, blue and green beads are mixed
together in the ratio 2:3:7. There are
1110 blue beads. How many beads are
there altogether?
( Answers: £72, 36, 100min, £36450 &
£72900, 4440 )
Mixed Exercise
The total sum of money is 2 + 5 = 7 parts so
Total sum = £4 × 7 = £28
2. Three partners in a business decide to split
the profits in the ratio of 1:3:4. The partner
with the largest share receives £ 35000. How
much do the other two receive?
1 part = £35000 ÷ 4
= £8750
One partner receives £8750
The third receives £8750 × 3 = £26250
Note: Always find one part first and use this to
answer the question.
J.Reed,Coventry University,October2000
1. Write 1·5:3 in its simplest form
2. Divide £45 in the ratio 2:3
3. Three students want to divide £140 in
the ratio 1:2:4. What is the largest
amount received?
4. 22kg of shopping is to be carried by
three people in the ratio 3:3:5. What is
the lightest load to be carried?
5. The profits from a job carried out by
three people are to be divided in the
ratio of the time spent by each. A spent
4 hours, B spent 6 hours and C spent 2
hours. If A receives £15 how much do
the other two receive?
( Answers: 1:2, £18 & £27, £80, 6kg, £22.50 &
£7.50 )